which holds for \(f\in {\mathcal {E}}^{\prime }(X) \cup S(X)\)  (see [1]}).
Next, the methods of the singular integral operator theory allow showing the existence of an operator \(T\)  in \({\mathcal {L}}(\mathbb {E}(X),\mathbb {E}(Y))\) , which agrees with the operator \(U\)  on \(S(X)\)  (or \(L^1_c(X)\) ).
